Standard Christian theology is that Christ died so that God could forgive our sins. But I think that Jesus said something a little more subtle: that he would die for “the forgiveness of sin.”
As I understand it, God is not about choosing those worthy to live in his presence, he is concerned with healing. A sin is a sin because it leaves a wound in the soul. That wound cannot be healed until we are ready to forgive the sin – to let it go so that it may be displaced by love. When that occurs, even the most vicious criminal becomes qualified to enter paradise.
Even better, though, is to hold on to the sin. It is to do as Jesus did – to allow the sin to take hold of us, and then to forgive it so that it may be suffused by love, and so made noble.
Death is a sin because is separates things that cherish one another. That cherishing reflects a mutually beneficial relationship. So for death to enforce such separation is to deny the parties those benefits, and thus to wound them.
In dying, Jesus allowed the servants of Death (the priests that slaughtered innocent creatures on the altar) to have their way with him, and forgave them. He suffused death with love, and so became the Prince of Peace.
How does that work? Because warring parties need to be separated. That can be accomplished in death, but what Jesus does is offer a spiritual refuge in which we can reflect until we figure out how to share strength with the ones we war against.
Sometimes, of course, that is our selves. Peace starts within, and when we accept Jesus, we allow him into our hearts and minds and grant him loving dominion over the conflicts that rage within us.
As Cain learned, it isn’t easy, but God understands that sin cannot be healed unless we wrestle with it. Terrible things happen: Cain murdered his brother Abel. But even then, that most heinous of sins was not punished with death. Instead, Cain was sent away to think, reflect, and become stronger.